CoCalc -- toto.ipynb

mon script toto

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Kernel: SageMath (stable)

In [2]:

def f(x):
    return x**2

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f(4)

Out[3]:

16

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2+2

Out[1]:

4

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Out[2]:

x

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%display typeset

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R.<x1, x2, x3, x4, x5>= QQ[]

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f= x1^2*(x2*x5 + x3*x4);f

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X= [0] + list(R.gens()); X

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g= lambda i, j, k, l, m : X[i]^2*(X[j]*X[k] + X[l]*X[m])

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g(1, 2, 5, 3, 4)

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F= g(1, 2, 5, 4, 3) + g(2, 1, 3, 4, 5)  + g(3, 1, 5, 2, 4) + g(4, 1, 2, 3, 5) + g(5, 1, 4, 2, 3)

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L= [F,    F(X[2], X[1], X[3], X[4], X[5]),    F(X[3], X[2], X[1], X[4], X[5]),       F(X[4], X[2], X[3], X[1], X[5]) ,       F(X[5], X[2], X[3], X[4], X[1]),     F(X[1], X[5], X[3], X[4], X[2]) ]

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len(L)

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S.<T>= R[]

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graal= prod([T - foo for foo in L])

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c= graal.coefficients()

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c[6]

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c[0]

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WARNING: Some output was deleted.

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symmetrize(c[0])

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